In conventional razor assembly, the blade support and the handle means are fixed and rigid and formed into a T-shaped frame. That is, the structure of this assembly cannot be folded or retracted into a compact assembly. As a result, the large volume of the razor assembly is inconvenient to be portable. In some similar type of razor assembly, a plastic cap is provided to protect the blade from accidental touching. However, the cap and the blade are easily dislocated from the razor assembly. Therefore, it must be paid additional attention while carrying along this razor assembly.